Problem solving is taken as a model for intellectual competence. It assumes that an understanding of the sources and character of individual differences in problem solving can inform special educational assessment and corrective techniques. The proposed research will test this model by examining problem solving in mentally retarded, normal, and gifted children relative to age, IQ and academic achievement. The proposal calls for problems for which there are independent measures of process and product, and for which solutions are non-trivial and instructible for children over a wide range of abilities. Two problems that meet these criteria are: (a) subject-paced memorization of isolated words intended to be recalled as a series; (b) subject-paced memorization of paired associates intended to be recalled as pairs. Two other problems will be developed around the Mitchell/Danks effect, using English sentences and prose passages to assess the generality of results; (c) self-paced listening comprehension; (d) self-paced listening for literal recall. Results will be correlated with IQ and academic achievement as an index of croww-validity. In 8 studies, children at various developmental levels will be tested for their current problem-solving skills; and again, with training, to assess learning potential. Training will focus on specific solutions and on general problem-solving. The research question is whether individual differences are stable across problems and over time. It is proposed to characterize such differences in terms of children's knowledge about their own thinking, and in terms of problem-solving skills. A finding that training influences either knowledge or skills will have direct implications for educational practice.